Check each paragraph in the region for unbalanced braces or dollar signs.

C-c {

Insert ‘{}’ and position point between them (tex-insert-braces).

C-c }

Move forward past the next unmatched close brace (up-list).

In TeX, the character ‘"’ is not normally used; we use
‘``’ to start a quotation and ‘''’ to end one. To make
editing easier under this formatting convention, TeX mode overrides
the normal meaning of the key " with a command that inserts a pair
of single-quotes or backquotes (tex-insert-quote). To be
precise, this command inserts ‘``’ after whitespace or an open
brace, ‘"’ after a backslash, and ‘''’ after any other
character.

If you need the character ‘"’ itself in unusual contexts, use
C-q to insert it. Also, " with a numeric argument always
inserts that number of ‘"’ characters. You can turn off the
feature of " expansion by eliminating that binding in the local
map (see section Customizing Key Bindings).

In TeX mode, ‘$’ has a special syntax code which attempts to
understand the way TeX math mode delimiters match. When you insert a
‘$’ that is meant to exit math mode, the position of the matching
‘$’ that entered math mode is displayed for a second. This is the
same feature that displays the open brace that matches a close brace that
is inserted. However, there is no way to tell whether a ‘$’ enters
math mode or leaves it; so when you insert a ‘$’ that enters math
mode, the previous ‘$’ position is shown as if it were a match, even
though they are actually unrelated.

TeX uses braces as delimiters that must match. Some users prefer
to keep braces balanced at all times, rather than inserting them
singly. Use C-c { (tex-insert-braces) to insert a pair of
braces. It leaves point between the two braces so you can insert the
text that belongs inside. Afterward, use the command C-c }
(up-list) to move forward past the close brace.

There are two commands for checking the matching of braces. C-j
(tex-terminate-paragraph) checks the paragraph before point, and
inserts two newlines to start a new paragraph. It outputs a message in
the echo area if any mismatch is found. M-x tex-validate-region
checks a region, paragraph by paragraph. The errors are listed in the
‘*Occur*’ buffer, and you can use C-c C-c or Mouse-2 in
that buffer to go to a particular mismatch.

Note that Emacs commands count square brackets and parentheses in
TeX mode, not just braces. This is not strictly correct for the
purpose of checking TeX syntax. However, parentheses and square
brackets are likely to be used in text as matching delimiters and it is
useful for the various motion commands and automatic match display to
work with them.